‘Building back better’ was a mantra promoted by many politicians and organisations at the height of the pandemic, but what would building back better actually look like from a public health perspective, and what are the political prospects? We argue for a new approach to the choice of a standard of proof (how much evidence is enough to warrant action on upstream influences on health inequalities); setting the bar high enough means there will never be enough evidence. We go on to argue for a focus on progressive taxation and expenditure and on rejecting the market-centred paradigm central to neoliberalism. We also argue for a critical perspective on claims that far-reaching policies are unaffordable because resources are scarce. We warn about intergenerational transmission of health inequalities, and about the perils of biological reductionism. We conclude with reasons for both pessimism and optimism about political change on the scale required.